Michael Struwe

TL;DR: Variational problems are part of our classical cultural heritage as discussed by the authors, and variational methods have been extensively studied in the literature, including lower semi-continuity results, the compensated compactness method, the concentration compactness methods, Ekeland's variational principle, and duality methods or minimax methods including the mountain pass theorems, index theory, perturbation theory, linking and extensions of these techniques to non-differentiable functionals and functionals defined on convex sets.

TL;DR: On demontre l'existence de solutions nontriviales de −Δu−λu=u|u| 2 * −2 dans Ω∈R n, u/∂Ω=0 arbitrairement proches des valeurs propres λ k de − Δ:H 0 1,2 (Ω)→H − 1 (λ) as discussed by the authors

TL;DR: The wave equation conservation laws Function spaces The linear wave equation wellposedness Semilinear wave equations Wave maps Wave maps with symmetry as discussed by the authors The wave equation Conservation laws and function spaces.

TL;DR: In this paper, it was shown that estimates for the pressure do not play an essential role in partial regularity results for the Navier-Stokes equations, and that the regularity of Scheffer, Caffarelli, Kohn, and Nirenberg is not essential.